91Ó°ÊÓ

Find all angles \(0^{\circ} \leq \theta<360^{\circ}\) which satisfy the given equation: $$\sin \theta=0$$

Find the values of the other five trigonometric functions of the acute angle \(A\) given the indicated value of one of the functions. $$\sin A=\frac{3}{4}$$

Prove that the hypotenuse is the longest side in every right triangle. (Hint: Is \(a^{2}+b^{2}>a^{2} ?\) )

Find all angles \(0^{\circ} \leq \theta<360^{\circ}\) which satisfy the given equation: $$\tan \theta=0.7813$$

Find all angles \(0^{\circ} \leq \theta<360^{\circ}\) which satisfy the given equation: $$\sin \theta=-0.6294$$

In which quadrant(s) do sine and cosine have the opposite sign?

Find all angles \(0^{\circ} \leq \theta<360^{\circ}\) which satisfy the given equation: $$\cos \theta=-0.9816$$

Find the values of the other five trigonometric functions of the acute angle \(A\) given the indicated value of one of the functions. $$\cos A=\frac{2}{\sqrt{10}}$$

If the lengths \(a, b\), and \(c\) of the sides of a right triangle are positive integers, with \(a^{2}+b^{2}=c^{2}\), then they form what is called a Pythagorean triple. The triple is normally written as \((a, b, c) .\) For example, \((3,4,5)\) and \((5,12,13)\) are well-known Pythagorean triples. (a) Show that \((6,8,10)\) is a Pythagorean triple. (b) Show that if \((a, b, c)\) is a Pythagorean triple then so is \((k a, k b, k c)\) for any integer \(k>0\). How would you interpret this geometrically? (c) Show that \(\left(2 m n, m^{2}-n^{2}, m^{2}+n^{2}\right)\) is a Pythagorean triple for all integers \(m>n>0\). (d) The triple in part(c) is known as Euclid's formula for generating Pythagorean triples. Write down the first ten Pythagorean triples generated by this formula, i.e. use: \(m=2\) and \(n=1 ; m=3\) and \(n=1,2 ; m=4\) and \(n=1,2,3 ; m=5\) and \(n=1\), \(2,3,4\)

Find the values of the other five trigonometric functions of the acute angle \(A\) given the indicated value of one of the functions. $$\sin A=\frac{2}{4}$$