Question

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Answer 1

Solution: Exercise 1.

Sine is Opposite/Hypotenuse.

Cosine is Adjacent/Hypotenuse.

Tangent is Opposite/Adjacent.

In that manner, we can find each trigonometric value.

$\therefore \sin\theta=\dfrac{9}{41} ,\cos\theta=\dfrac{40}{41} ,\tan\theta=\dfrac{9}{40}$

Now we have three multiplicative inverse trigonometry values.

$\therefore \csc\theta=\dfrac{41}{9} ,\sec\theta=\dfrac{41}{40} ,\cot\theta=\dfrac{40}{9}$

Solution: Exercise 2.

In fact, solution 2 doesn't have just one value as the answer.

$\sin A=\dfrac{a}{c} =\dfrac{3}{5} ,\cos A=\dfrac{b}{c} =\dfrac{4}{5}$

There are infinitely many solutions, $a=3k,b=4k,c=5k$. Try putting some values for $k$ and make some right triangles.

$\tan B=\dfrac{b}{a} =\dfrac{3}{2}$

This has infinitely many solutions as well, $a=2k,b=3k,c=\sqrt{13} k$. For positive values of $k$, this generates infinitely many triangles.

Answer 2

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