Trigonometry Problems - Basics, Advanced & Examples

What is right triangle
1) 5, 11, 13
2) 9, 12, 14
3) 8, 15, 17
4) 10, 16, 19

Solve ${\displaystyle (1+\cos x)\frac{\tan x}{2}=\sin x}$

Jamie was supposed to have completed a portfolio of geometric constructions during spring break. She started this construction of a triangle center on the first day of her vacation and then forgot about it. Help her complete her portfolio entry. What is the name of the triangle center that Jamie constructed (point X )? What special properties does it have? Compute the volume of the figure at right.

Prove the identity. ${\displaystyle \frac{{\tan }^{2}x}{\sec x}=\sec x-\cos x}$

simplify $(\cos x/1+\sin x)+(1+\sin x/\cos x)$

If $f(\theta )=\sin \theta =0.2$
Find $f(\theta +\pi )$

Given theta is an acute angle such that sin theta = ${\displaystyle \frac{5}{13}}$ find the value of $\tan (\theta -\pi /4)$

Find the value of x
${\displaystyle \cos 35\cdot =\frac{21}{x}}$

Suppose that ${\displaystyle m\mathrm{\angle }BCA={70}^{\circ }}$, and $x=33$ cm and $y=47$ cm. What is the degree measure of ${\displaystyle \mathrm{\angle }ABC}$?

The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ${\displaystyle f{t}^2}$) and has a height of 481 ft . Ifthe volume of a pyramid is given by the expression $V=(\frac{1}{3})$bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides ____________________.

The prism has a cross-sectional area in the shape of a sector. Calculate: a. the radius rr cm,
b. the cross-sectional area of the prism,
c. the total surface area of the prism,
d. the volume of the prism

State the form of the law of cosines used to solve a triangle for which all three sides are given (SSS).

Solve ${\displaystyle \cos 30\cdot \frac{\sin (-50)}{\tan 70}}$

Use a calculator to find the value of the trigonometric function csc 1 to four decimal places.

An equilateral triangle is inscribed in a circle of radius 4r. Express the area A within the circle but outside the triangle as a function of the length 5x of the side of the triangle.

The ___ is formed by the congruent legs of an isosceles triangle.

In triangle ABC, a=5, ${\displaystyle M<B=92°}$, c=3. Find b.

A ship sets out to sail to a point 120 km due north. An unexpected storm blows the ship to a point 100 km due east of its starting point. (a) How far and (b) in what direction must it now sail to reach its original destination?

$\sec \theta =3,\sin \theta >0$
Find $\sin \theta$