SOLUTION: If cosθ = 4/5 and θ is an acute angle, find the exact value of cos(θ-45°).
Please show me how to solve other problems like this, I'm trying to learn Algebra 2 by
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Question 1106055: If cosθ = 4/5 and θ is an acute angle, find the exact value of cos(θ-45°).
Please show me how to solve other problems like this, I'm trying to learn Algebra 2 by myself and my textbook doesn't have enough examples.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
theta is acute, then theta < 90 degrees
:
cos theta = 4/5
:
use the inverse trig function to find theta
:
cos^(-1) (4/5) = 36.87 degrees
:
36.87 - 45 = -8.13
:
cos(-8.13) = 0.99
:
Note negative angles are measured clockwise, so instead of taking the cosine of -8.13, we could haave taken the cosine of (360 - 8.13) and get the same answer
:
if your teacher does not want you to use inverse trig functions, you can use trig identities
:
sin^2 theta + cos^2 theta = 1
:
sin^2 theta + (4/5)^2 = 1
:
sin^2 theta = 1 - 16/25 = 9/25
:
sin theta = 3/5
:
cos(theta-45) = cos theta * cos 45 + sin theta * sin 45
:
cos(theta-45) = (4/5) * 0.7071 + (3/5) * 0.7071 = 0.99
:
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