Try the following ACT math practice question that tests your understanding of evaluating trigonometric expressions in the context of right triangles.

In the right triangle $ABC$ shown below, what is the value of $1 – \cos^2{A} – \cos^2{B}$ ?

1. $\quad -1$
2. $\quad \displaystyle -\frac{1}{2}$
3. $\quad \displaystyle \hskip 0.8em 0$
4. $\quad \displaystyle \hskip 0.8em 1$
5. $\quad \displaystyle \hskip 0.6em \frac{1}{2}$

Choice C

Video explanation

Try this ACT math practice question that tests your ability to find the x-intercepts of circles.

The circle $(x+1)^2+(y-2)^2=29$ intersects the $x-$axis in two points, one of which is $(4,0)$. What are the coordinates of the other point where the circle intersects the $x-$axis?

1. $\quad (-7, 0)$
2. $\quad (-6, 0)$
3. $\quad (-\sqrt{29}, 0)$
4. $\quad (-5, 0)$
5. $\quad (-4, 0)$

Choice B

Video explanation

Try this ACT math practice question that tests your ability to algebraically simplify a trigonometric expression using trigonometric identities.

$$\dfrac{\cos \theta}{1 – \sin \theta} \quad – \quad \dfrac{\sin \theta}{\cos \theta}$$

When $\cos \theta \neq 0$ and $\sin \theta \neq 1$, which of the following is equivalent to the expression above?

1. $\quad \sec \theta$
2. $\quad \csc \theta$
3. $\quad \cos \theta$
4. $\quad \cos^{2} \theta$
5. $\quad \dfrac{\cos \theta – \sin \theta}{(\cos \theta)(1 – \sin \theta)}$

Choice A

Video explanation

Try this ACT math practice question on the topics of right triangles, algebraic translation and manipulation.

The perimeter of a right triangle is $18$ inches, and one of the legs of the triangle is $6$ inches long. How many inches longer is the hypotenuse than the length of the shortest leg ?

1. $\quad 1.5$
2. $\quad 2$
3. $\quad 3$
4. $\quad 3.5$
5. $\quad 4$

Choice C

 
Here is a link to the playlist of video explanations to all of the math questions in the 2019 December ACT (Form C03) Test.