# Evaluating the Six Trigonometric Functions

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 The terminal side of an angle in standard position passes through P(-3, -4). What is the value of tangent of theta? tangent of theta = 4/3 Francesca drew point (-2, -10) on the terminal ray of angle theta, which is in standard position. She found values for the six trigonometric functions using the steps below. IT IS NOT She made her first error in step 2 because she should have used a negative value for r. The point P(x, y) lies on the terminal side of an angle theta = 3pi/4 in standard position. What are the signs of the values of x and y? x is negative, and y is positive. If tangent of theta = -3/8, which expression is equivalent to cotangent of theta? 1/(-3/8) Given that tangent of theta = -1, what is the value of secant of theta, for 3pi/2 < theta < 2pi? sqrt of 2 If sine of theta equals -0.7660, which of the following represents an approximate value of tangent of theta, for 180 degrees < theta < 270 degrees? 1.1916 Keisha and David each found the same value for cosine of theta, as shown below, given sine of theta = -8/17 Both procedures are correct. Given that secant of theta = -37/12, what is the value of cotangent of theta , for pi/2 < theta < pi? -12/35 Given that sine of theta = 21/29, what is the value of cosine of theta, for 0° < theta < 90°? 20/29 Fatima wants to find the value of sine of theta, given cotangent of theta = 4/7 Which identity would be best for Fatima to use? 1 + cotangent-squared of theta = cosecant-squared of theta Three trigonometric functions for a given angle are shown below. sine of theta = -77/85 cosine of theta = 36/85 tangent of theta = -77/36 What are the coordinates of point (x, y) on the terminal ray of angle theta, assuming that the values above were not simplified? (36, -77) The terminal side of an angle in standard position passes through P(15, -8). What is the value of sine of theta? sine of theta = -8/17 The point (-sqrt of 2/2, sqrt of 2/2) is the point at which the terminal ray of angle theta intersects the unit circle. What are the values for the cosine and cotangent functions for angle theta? cosine of theta = -sqrt2/2, cotangent of theta=-1 Based on Pythagorean identities, which equation is true? cotangent-squared of theta – cosecant-squared of theta = -1 The point P(x, y) lies on the terminal side of an angle theta = -60° in standard position. What are the signs of the values of x and y? x is positive, and y is negative. Which Pythagorean identity is correct? tan-squared (theta) + 1 = sec-squared (theta)

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