Unit 4 Lesson 1: Trigonometry Fundamentals and Identities

Flashcards based on lecture notes covering trigonometric ratio definitions, values for specific angles (30, 45, 60 degrees), and the use of identities to solve for unknown ratios.

Based on the transcript, what is the ratio definition for $\sin(A)$?

$$\frac{\text{opposite}}{\text{hypotenuse}}$$

What is the ratio definition for $\csc(A)$ according to the notes?

$$\frac{\text{hypotenuse}}{\text{opposite}}$$

What is the ratio definition for $\cos(A)$?

$$\frac{\text{adjacent}}{\text{hypotenuse}}$$

What is the ratio definition for $\sec(A)$?

$$\frac{\text{hypotenuse}}{\text{adjacent}}$$

What is the ratio definition for $\tan(A)$?

$$\frac{\text{opposite}}{\text{adjacent}}$$

What is the ratio definition for $\cot(A)$?

$$\frac{\text{adjacent}}{\text{opposite}}$$

According to the transcript, what is the value of $\sin(30)$?

$$\frac{1}{2}$$

According to the transcript, what is the value of $\cos(30)$?

$$\frac{3}{2}$$

What is the value provided for $\tan(30)$ in the notes?

$$\frac{3}{3}$$

What is the value of $\sin(45)$ as written in the notes?

$$\frac{2}{2}$$

What is the value of $\cos(45)$ as written in the notes?

$$\frac{2}{2}$$

What is the value of $\tan(45)$?

$$1$$

What is the value provided for $\sin(60)$?

$$\frac{3}{2}$$

What is the value provided for $\cos(60)$?

$$\frac{1}{2}$$

What is the value provided for $\tan(60)$?

$$\frac{3}{2}$$

If $\theta$ is an acute angle and $\sin(\theta) = 0.6$, what are the values of $\cos(\theta)$ and $\tan(\theta)$ as indicated in the practice problems?

$\cos(\theta) = 0.8$ and $\tan(\theta) = 0.75$

If $\theta$ is an acute angle and $\cos(\theta) = \frac{5}{13}$, what are the values of $\sin(\theta)$ and $\tan(\theta)$?

$\sin(\theta) = \frac{12}{13}$ and $\tan(\theta) = \frac{12}{5}$

What is the value of $\cot(\theta)$ if $\tan(\theta) = \frac{1}{3}$ for an acute angle?

$$3$$

What is the value of $\sec(\theta)$ if $\tan(\theta) = 2$ for an acute angle?

$$\sqrt{5}$$