Question

Find the smallest positive angle theta such that cosine of theta equals sine of negative 203 degrees. Give your answer in degrees.

a) theta equals 22 degrees
b) theta equals 203 degrees
c) theta equals 68 degrees
d) theta equals 112 degrees

Answer 1

The smallest positive angle θ such that cosine(θ) equals sine(-203°) is 247°.

Step-by-step explanation:

The smallest positive angle θ such that cosine(θ) equals sine(-203°) can be determined by finding the reference angle. We know that cosine(θ) equals sine(-θ) for any angle θ. To find the reference angle, we take the absolute value of -203° which gives us 203°. Next, we find the complementary angle by subtracting the reference angle from 90° which gives us 90° - 203° = -113°. Since we are looking for the smallest positive angle, we add 360° to -113° which gives us 247°. Therefore, the smallest positive angle θ is 247°.