Question

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -510°

Accepted Answer

Step 1: Understand that the angle given is -510°, which is a negative angle. To find the trigonometric functions, first find a positive coterminal angle by adding 360° repeatedly until the angle is between 0° and 360°. Calculate: $$-510° + 360° = -150°$$, then add 360° again: $$-150° + 360° = 210°. So$$, the coterminal angle is $$210°. $$Step 2: Identify the reference angle for $$210°. $$Since $$210° is in $$the third quadrant (between 180° and 270°), the reference angle is $$210° - 180° = 30°. $$Step 3: Recall the exact values of the six trigonometric functions for the reference angle $$30°$$: 
- $$\sin 30° = \frac{1}{2}$$
- $$\cos 30° = \frac{\sqrt{3}}{2}$$
- $$	an 30° = \frac{1}{\sqrt{3}}$$
- $$\csc 30° = 2$$
- $$\sec 30° = \frac{2}{\sqrt{3}}$$
- $$\cot 30° = \sqrt{3}$$ Step 4: Determine the signs of the trigonometric functions in the third quadrant. In the third quadrant, both sine and cosine are negative, but tangent is positive. Therefore:
- $$\sin 210° = -\sin 30°$$
- $$\cos 210° = -\cos 30°$$
- $$	an 210° = +	an 30°$$ Step 5: Use the reciprocal identities to find the other three functions:
- $$\csc 210° = \frac{1}{\sin 210°}$$
- $$\sec 210° = \frac{1}{\cos 210°}$$
- $$\cot 210° = \frac{1}{	an 210°}$$
Remember to rationalize denominators where applicable.

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -510°

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Reference Angles and Coterminal Angles

Signs of Trigonometric Functions in Different Quadrants

Rationalizing Denominators