University:
North Central College
Course:
MATH 152 | Calculus II
Academic year:

2024
Views:

401

Pages:

2
Author:

nesikhiyawl0

Question 1 Let theta be an angle in standard position, sin θ < 0, cos θ > 0. Name the quadrant in which theta lies. Answer as we know that: (1) in first quadrant all trigonometric functions are positive. (2) in second quadrant sine and cosecant trigonometric functions are positive and rest trigonometric functions are negative. (3) in third quadrant tangent and cotangent trigonometric functions are positive and rest trigonometric functions are negative. (4) in fourth quadrant cosine and secant trigonometric functions are positive and rest trigonometric functions are negative. as sin θ < 0, cos θ > 0, therefore we can say that the angle theta lies in the fourth quadrant. therefore, the quadrant in which theta lies is fourth quadrant. Question 2 The trigonometric functions sec (135°) Answer To find the value of the trigonometric functions, first, convert sec function in terms of cos (θ). Use the identity sec (θ) = 1 / cos (θ) We have θ = 135° = 90° + 45° cos (135°) = cos (90° + 45°) = -sin (45°) {cos (90° + θ) = -sin (θ)} = -1/√2 Now sec (θ) = 1 / cos (θ) sec (135°) = 1 / cos (135°) = 1 / (-1/√2) = -√2 = -1.4142 Question 3 Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t. sin t = 3/4 and cos t = √7/4 Answer Consider the given trigonometric function sin t and cos t. The other trigonometric functions values are find as, Use the trigonometric formula, tan t = sin t / cos t csc t = 1 / sin t sec t = 1 / cos t cot t = cos t / sin t Now, substitute the given trigonometric function values in the above formula, Since sin t = 3/4 and cos t = √7/4 Thus, tan t = sin t / cos t = (3/4) / (√7/4) = 3 / √7 csc t = 1 / sin t = 1 / (3/4) = 4/3 sec t = 1 / cos t = 1 / (√7/4) = 4 / √7 cot t = cos t / sin t = (√7/4) / (3/4) = √7/3 Question 4 Find the exact value of sin 60°. Answer Use the following trivial identity: sin (60°) = √3/2 Decimal: 0.86602...