Question

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -2205°

Accepted Answer

Step 1: Understand that the angle given is -2205°, which is a negative angle. To find the trigonometric functions, first convert this angle to a positive coterminal angle between 0° and 360° by adding multiples of 360° until the angle lies within this range. Use the formula: $$	heta_{coterminal} = 	heta + 360k$$, where $$k is an $$integer chosen to make $$	heta_{coterminal}$$ between 0° and 360°. Step 2: Calculate the coterminal angle by adding 360° repeatedly to -2205° until the result is between 0° and 360°. This will give you an equivalent angle that has the same trigonometric values as -2205°. Step 3: Once you have the coterminal angle, determine the reference angle. The reference angle is the acute angle formed between the terminal side of the coterminal angle and the x-axis. This helps in finding the exact values of the trigonometric functions. Step 4: Identify the quadrant in which the coterminal angle lies. The signs of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) depend on the quadrant. Recall the ASTC rule (All Students Take Calculus) to determine the signs. Step 5: Use known exact values of trigonometric functions for standard angles (like 30°, 45°, 60°, etc.) and apply the appropriate sign based on the quadrant to find the exact values of all six trigonometric functions. Rationalize denominators if necessary.

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. -2205°

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angle Reduction Using Coterminal Angles

Definition of the Six Trigonometric Functions

Rationalizing Denominators