Question 155582: Given that sine theta equals 4/5 and theta is acute, find the value of the remaining 5 trigonometry functions.
Found 2 solutions by Alan3354, ilana:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Given that sine theta equals 4/5 and theta is acute, find the value of the remaining 5 trigonometry functions
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If the sine if 4/5, then the side opposite is 4 and the hypotenuse is 5. This means it's the 3, 4, 5 right triangle (or similar, such as 6, 8, 10). Solve for the other side using Pythagoras if there's doubt.
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So:
cos = 3/5
tan = 4/3
cot = 3/4
sec = 5/3
csc = 5/4
Answer by ilana(307)  (Show Source):
You can put this solution on YOUR website! Draw a picture of the triangle. Since the angle is acute, it is in the first quadrant. Since sin(theta)=4/5, you can say the side opposite theta is 4 and the hypotenuse is 5. Now you are just missing one side. You can use the Pythagorean Theorem to solve for that side, or you could recognize that this is a 3-4-5 triangle. Either way, the adjacent side (along the x-axis) is 3. Now you know each side's measure. So Cos(theta)=adjacent/hypotenuse=3/5 and tan(theta)=opp/adj=4/3. Use these to find cosecant, secant, and cotangent.
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