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Calculus/Trig Functions
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Question
Find the 6 trigonometric values of Θ = cos^−1 (3/7).
Give exact answer.
They might mean the second approach I took, or they might mean to find the six trig functions on an anlge between 0° and 90° (0 and π/2 radians).
Approach 1 (probably right)
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If the near side on the triangle is 3, the hypoteneuse is 7 and the far side is sqrt(7²-3²)=√40. These would be exact answers.
The trig functions would be
Θ=sin^-1(√40/7),
Θ=cos^-1(4/7),
Θ=tan^-1(√40/4),
Θ=ctn^-1(7/√40,)
Θ=sec^-1(7/4), and
Θ=csc^-1(7/√40).
(by the way, they aren't on my keyboard, but ° is alt-248, π is alt-227, Θ is alt-233, √ is alt-251 and ² is alt-233)
(or) Approach 2
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Second, there is an angle between 0 and 90 degrees (0 anbd pi/2 radians). Note that I can't figure out how to express them exactly as real numbers.
I'm not sure how to find it exactly and there are only 2 values between 0° and 360° degrees. I do know how to find the six values, though, and that's by adding 360° and 720° to the first two angles.
It is 64.62306647° (1.127885283 radians). Let's call it angle a.
1) a
2) (180-a)°
3) (360+a)°
4) (540-a)°
5) (720+a)°
6) (900-a)°
I hope one of these is the right way to get six values.
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