MATH SOLVE

3 months ago

Q:
# Find the values of the trigonometric functions of θ from the information given.cos(θ) = 7/17, sin(θ) < 0

Accepted Solution

A:

Answer:sin(θ) = -(4√15)/17cos(θ) = 7/17 . . . . . . . giventan(θ) = -(4√15)/7csc(θ) = -(17√15)/60sec(θ) = 17/7cot(θ) = -(7√15)/60Step-by-step explanation:The relationship between sine and cosine is ... sin² + cos² = 1Solving for sine gives ... sin = ±√(1 -cos²)In this problem, we want the negative root. sin(θ) = -√(1 -(7/17)²) = -√(240/289) = -(4√15)/17 tan(θ) = sin(θ)/cos(θ) = ((-4√15)/17)/(7/17) = -(4√15)/7___And the inverse functions are ... sec(θ) = 1/cos(θ) = 17/7 csc(θ) = 1/sin(θ) = -17/(4√15) = -(17√15)/60 cot(θ) = 1/tan(θ) = -(7√15)/60_____Of course, you're aware that 1/√15 = (√15)/15.