Find the exact values of cos 150° and sin 150°

We have to find the values of cos 150 and sin150

Solution

We know that
150 =180−30

cos 150

We know that

cos (180 – Θ)= – cosΘ

cos 150 = cos (180-30)

= – cos 30

We know that cos 30 =√3/2

Hence, cos 150 = – cos 30 = -√3/2

Sin 150

We know that

sin (180 – Θ)= sin Θ

sin150=sin(180−30)

=sin30

sin30=1/ 2

Note

The value of sin 30 degrees and sin 150 degrees are equal.

Sin 30 = sin 150 = 1/2

Both are equal because the reference angle for 150 is equal to 30 for the triangle formed in the unit circle. The reference angle is formed when the perpendicular is dropped from the unit circle to the x-axis, which forms a right triangle.

Since, the angle 150 degrees lies on the IInd quadrant, therefore the value of sin 150 is positive. The internal angle of the triangle is 180 – 150=30, which is the reference angle.

The value of sine in the other two quadrants, i.e. 3rd and 4th are negative.

Answer

Hence, cos 150 = -√3/2 and sin 150= 1/2

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