How do you find $$\tan(\theta)$$ if $$\sin(\theta)=-\frac{3}{5}$$ and $$\cos(\theta)>0$$ ?

Use the identity $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$ . Since $$\sin(\theta) = -\frac{3}{5}$$ , find $$\cos(\theta)$$ using $$\sin^2(\theta) + \cos^2(\theta) = 1$$ .

What is the exact value of $$\tan(\theta)$$ if the terminal side of $$\theta$$ contains the point (-9,-40)?

Use the formula $$\tan(\theta) = \frac{y}{x}$$ . Here, $$y = -40$$ and $$x = -9$$ , so $$\tan(\theta) = \frac{-40}{-9} = \frac{40}{9}$$ .

What is the definition of tangent in a right triangle?

Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ .

How do you determine the quadrant of an angle given in radians?

To determine the quadrant, convert the angle to degrees or analyze the reference angle. Angles between 0 and 90 degrees are in quadrant I, 90 to 180 in II, 180 to 270 in III, and 270 to 360 in IV.

What is the relationship between sine, cosine, and tangent?

The relationship is given by the identity: $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$ .

How do you find the reference angle for an angle in the third quadrant?

The reference angle is found by subtracting 180 degrees (or $$\pi$$ radians) from the angle.

What is the value of $$\sin(40)$$ in a right triangle with hypotenuse 28 and side w?

Using the equation $$\sin(40) = \frac{w}{28}$$ , you can find w by rearranging to $$w = 28 \cdot \sin(40)$$ .

What is the significance of the terminal side of an angle?

The terminal side of an angle is the position of the angle after it has been rotated from the initial side, which is usually along the positive x-axis.

How do you calculate the sine of an angle using a right triangle?

Identify the opposite side and the hypotenuse, then use the formula: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

What is the formula to find the length of a side in a right triangle using cosine?

Use the formula: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ , rearranging to find the adjacent side.

Math 3H Unit 6 Part I REVIEW Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula to find the length of side AB in a right triangle?

Back

2.

FLASHCARD QUESTION

Front

Back

The angle lies in the III quadrant.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the correct equation to solve for side w in a right triangle with angle 40 degrees and hypotenuse 28?

Back

6.

FLASHCARD QUESTION

Front

What is the definition of sine in a right triangle?

Back

7.

FLASHCARD QUESTION

Front

What is the definition of cosine in a right triangle?

Back

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