Sin 120 in fraction

Use #tan theta = sin(theta)/cos(theta)# From a trig circle or a #30^@-60^@-90^@# triangle in the second quadrant: #tan 120^@ = (sqrt(3)/2)/(-1/2) = sqrt(3)/2 *-2/1 = -sqrt(3)# From a trig circle or a #45^@-45^@-90^@# triangle in the second quadrant: #tan 135^@ = (sqrt(2)/2)/(-sqrt(2)/2) = sqrt(2)/2 * -2/sqrt(2) = -1# From a trig circle or a #30^@-60^@-90^@# triangle in the second quadrant: #tan 150^@ = (1/2)/(-sqrt(3)/2) = 1/2 * -2/sqrt(3) = -1/sqrt(3) = -1/sqrt(3) * sqrt(3)/sqrt(3) = -sqrt(3)/3# Let's use the unit circle to find the values ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)(tan(120^circ)# We have the values of #sin(120^circ) and cos(120^circ)# So, use the identity #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(120^circ)=(sin(120^circ))/(cos(120^circ))# #rarrtan(120^circ)=(sqrt(3)/2)/(-1/2)# #rarrtan(120^circ)=sqrt(3)/2*-2/1# #rarrtan(120^circ)=-cancel2sqrt(3)/cancel2# #color(blue)(rArrtan(120^circ)=-sqrt(3)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(orange)(tan(135^circ)# #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(135^circ)=(sin(135^circ))/(cos(135^circ))# #rarrtan(135^circ)=(sqrt(2)/2)/(-sqrt(2)/2)# #rarrtan(135^circ)=2/sqrt2*-2/sqrt(2)# #rarrtan(135^circ)=-cancel((2sqrt2)/(2sqrt2)# #color(orange)(rArrtan(135^circ)=-1# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(purple)(tan(150^circ)# #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(150^circ)=(sin(150^...

Sin 120 In Mathematics, trigonometry is a branch that deals with the study of measures of right-angle triangles such as length, height and angles. Trigonometry has enormous applications in various fields, such as Architecture, Navigation systems, sound waves detections, and so on. In this article, let us discuss the value of sin 120, and the various methods which are used to find the sin 120 values using other • • • • • How to Derive the Value of Sin 120 Degrees? The sin 120-degrees value can be identified using either unit circle or with the help of other trigonometric angles such as 60, 180 degrees and so on. Let us consider the value 120 degrees in the cartesian plane. We know that the cartesian plane is divided into four quadrants. The value 120 degrees falls on the second quadrant. As the value of sine function in the second quadrant takes the positive value, the value of sin 120 degrees should be a positive value. By using the unit circle, the value of sin 120 can be calculated. We know the radius of the circle is the hypotenuse of the right triangle which is equal to the value 1. From the cartesian plane, we take, x= cos and y = sin By looking at the diagram given above, the value of sin 60 is equal to the value of sin 120. It means that, sin 60 = sin 120 = √3/2. Method 1 Another method to find the value of sin 120 degrees is by using the other angles of the sine functions such as 60 degrees and 180 degrees which are taken from the We know that 180° – 60° = 120Â...

Find the value of the given trigonometric ratio by using the required identity : Given trigonometric ratio: sin 135 ∘ sin 135 ∘ can be expressed as, sin 135 ∘ = sin ( 90 ∘ + 45 ∘ ) Using the identity, sin ⁡ ( A + B ) = sin ⁡ A cos ⁡ B + cos ⁡ A sin ⁡ B we can write, sin ( 90 ∘ + 45 ∘ ) = sin 90 ∘ × cos 45 ∘ + cos 90 ∘ × sin 45 ∘ We know that, sin ⁡ 45 ∘ = 1 2 cos ⁡ 45 ∘ = 1 2 sin ⁡ 90 ∘ = 1 cos ⁡ 90 ∘ = 0 By substituting the above values we get, sin ( 90 ∘ + 45 ∘ ) = 1 × 1 2 + 0 × 1 2 ⇒ sin ( 135 ∘ ) = 1 2 Hence, the value of sin ⁡ 135 ∘ is 1 2 .

Sin 120 In Mathematics, trigonometry is a branch that deals with the study of measures of right-angle triangles such as length, height and angles. Trigonometry has enormous applications in various fields, such as Architecture, Navigation systems, sound waves detections, and so on. In this article, let us discuss the value of sin 120, and the various methods which are used to find the sin 120 values using other • • • • • How to Derive the Value of Sin 120 Degrees? The sin 120-degrees value can be identified using either unit circle or with the help of other trigonometric angles such as 60, 180 degrees and so on. Let us consider the value 120 degrees in the cartesian plane. We know that the cartesian plane is divided into four quadrants. The value 120 degrees falls on the second quadrant. As the value of sine function in the second quadrant takes the positive value, the value of sin 120 degrees should be a positive value. By using the unit circle, the value of sin 120 can be calculated. We know the radius of the circle is the hypotenuse of the right triangle which is equal to the value 1. From the cartesian plane, we take, x= cos and y = sin By looking at the diagram given above, the value of sin 60 is equal to the value of sin 120. It means that, sin 60 = sin 120 = √3/2. Method 1 Another method to find the value of sin 120 degrees is by using the other angles of the sine functions such as 60 degrees and 180 degrees which are taken from the We know that 180° – 60° = 120Â...

Find the value of the given trigonometric ratio by using the required identity : Given trigonometric ratio: sin 135 ∘ sin 135 ∘ can be expressed as, sin 135 ∘ = sin ( 90 ∘ + 45 ∘ ) Using the identity, sin ⁡ ( A + B ) = sin ⁡ A cos ⁡ B + cos ⁡ A sin ⁡ B we can write, sin ( 90 ∘ + 45 ∘ ) = sin 90 ∘ × cos 45 ∘ + cos 90 ∘ × sin 45 ∘ We know that, sin ⁡ 45 ∘ = 1 2 cos ⁡ 45 ∘ = 1 2 sin ⁡ 90 ∘ = 1 cos ⁡ 90 ∘ = 0 By substituting the above values we get, sin ( 90 ∘ + 45 ∘ ) = 1 × 1 2 + 0 × 1 2 ⇒ sin ( 135 ∘ ) = 1 2 Hence, the value of sin ⁡ 135 ∘ is 1 2 .

Use #tan theta = sin(theta)/cos(theta)# From a trig circle or a #30^@-60^@-90^@# triangle in the second quadrant: #tan 120^@ = (sqrt(3)/2)/(-1/2) = sqrt(3)/2 *-2/1 = -sqrt(3)# From a trig circle or a #45^@-45^@-90^@# triangle in the second quadrant: #tan 135^@ = (sqrt(2)/2)/(-sqrt(2)/2) = sqrt(2)/2 * -2/sqrt(2) = -1# From a trig circle or a #30^@-60^@-90^@# triangle in the second quadrant: #tan 150^@ = (1/2)/(-sqrt(3)/2) = 1/2 * -2/sqrt(3) = -1/sqrt(3) = -1/sqrt(3) * sqrt(3)/sqrt(3) = -sqrt(3)/3# Let's use the unit circle to find the values ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)(tan(120^circ)# We have the values of #sin(120^circ) and cos(120^circ)# So, use the identity #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(120^circ)=(sin(120^circ))/(cos(120^circ))# #rarrtan(120^circ)=(sqrt(3)/2)/(-1/2)# #rarrtan(120^circ)=sqrt(3)/2*-2/1# #rarrtan(120^circ)=-cancel2sqrt(3)/cancel2# #color(blue)(rArrtan(120^circ)=-sqrt(3)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(orange)(tan(135^circ)# #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(135^circ)=(sin(135^circ))/(cos(135^circ))# #rarrtan(135^circ)=(sqrt(2)/2)/(-sqrt(2)/2)# #rarrtan(135^circ)=2/sqrt2*-2/sqrt(2)# #rarrtan(135^circ)=-cancel((2sqrt2)/(2sqrt2)# #color(orange)(rArrtan(135^circ)=-1# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(purple)(tan(150^circ)# #color(brown)(tan(theta)=( sin(theta))/(cos(theta))# #rarrtan(150^circ)=(sin(150^...