How do you solve the equation $$3\tan^2\theta - 1 = 0$$ for $$0 \\leq \theta

First, isolate $$\tan^2\theta$$ : $$\tan^2\theta = \frac{1}{3}$$ . Then, take the square root to find $$\tan\theta = \frac{1}{\text{sqrt}(3)}$$ , which gives the angles: $$\theta = \frac{\text{π}}{6}, \frac{5\text{π}}{6}, \frac{7\text{π}}{6}, \frac{11\text{π}}{6}$$ .

How do you simplify $$\text{cos}^2 x (\text{sec}^2 x - 1)$$ ?

Using the identity $$\text{sec}^2 x = 1 + \text{tan}^2 x$$ , we can simplify: $$\text{cos}^2 x (\text{sec}^2 x - 1) = \text{cos}^2 x \text{tan}^2 x = \text{sin}^2 x$$ .

What is the amplitude of a sine or cosine function?

The amplitude of a sine or cosine function is the maximum distance from the midline to the peak (or trough) of the graph. It is given by the coefficient in front of the sine or cosine function.

What is the period of the sine and cosine functions?

The period of the sine and cosine functions is $$2\text{π}$$ .

What is the relationship between the angles in a right triangle?

In a right triangle, the sum of the angles is always $$90^\text{°}$$ (the right angle) plus the other two angles.

What is the definition of amplitude in trigonometric functions?

Amplitude is defined as half the distance between the maximum and minimum values of the function.

How do you find the exact value of $$\text{sec} \theta$$ given a point on the terminal side?

Use the coordinates of the point (x, y) to find the hypotenuse r: $$r = \text{sqrt}(x^2 + y^2)$$ , then calculate $$\text{sec} \theta = \frac{r}{x}$$ .

What is the unit circle and its significance in trigonometry?

The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. It is significant because it provides a way to define the trigonometric functions for all angles.

What is the definition of cosine (cos)?

The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. In terms of the unit circle, it is the x-coordinate of the point on the circle corresponding to that angle.

What is the definition of sine (sin)?

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. In terms of the unit circle, it is the y-coordinate of the point on the circle corresponding to that angle.

Semester 1 Final Exam Mixed Review PCA

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF.TF.A.2, HSG.SRT.C.6, HSF-IF.C.7E

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FLASHCARD QUESTION

Front

What is the definition of secant (sec)?

Back

Tags

CCSS.HSG.SRT.C.6

FLASHCARD QUESTION

Front

Given a point (x, y) on the terminal side of an angle, how do you find the secant of that angle?

Back

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

What is the range of the secant function?

Back

FLASHCARD QUESTION

Front

What is the formula for the tangent function in terms of sine and cosine?

Back

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

What is the Pythagorean identity involving sine and cosine?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

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Back

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