Answer:
- sin(θ) = 4/5
- cos(θ) = 3/5
- cot(θ) = 3/4
Explanation:
Given tan(θ) = 8/6 for θ in the first quadrant, you want the values of sin(θ), cos(θ), and cot(θ).
Tangent
The mnemonic SOH CAH TOA is useful for this. It tells you ...
Tan = Opposite/Adjacent
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
The tangent of θ is given as a ratio (8/6). We can use the values in this ratio as the sides of the triangle. The diagram in the first attachment shows this. We recognize this triangle as a 3-4-5 triangle, so we know the length of the hypotenuse is 10 units. (Or, you could use the Pythagorean theorem to compute the length of the hypotenuse.)
Sine
As we learned above, the sine ratio is ...
sin(θ) = 8/10 = 4/5
Cosine
As we learned above, the cosine ratio is ...
cos(θ) = 6/10 = 3/5
Cotangent
The cotangent is the inverse of the tangent:
cot(θ) = 1/(8/6) = 6/8 = 3/4
The trig values you want are ...
- sin(θ) = 4/5
- cos(θ) = 3/5
- cot(θ) = 3/4
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Additional comment
Your calculator can also help you figure this out. The second attachment shows the result. (The angle shown is in degrees. Using radians gives the same result.)
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