Topic 7 Trigonometric Functions

Presentation

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Mathematics

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10th - 12th Grade

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Easy

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CCSS

HSF.TF.C.8, HSG.SRT.C.8

Standards-aligned

Erich Myers

Used 11+ times

FREE Resource

9 Slides • 3 Questions

Topic 7 Trigonometric Functions

Sine and Cosine

Sine and Cosine are defined as:

Sine is the opposite side divided by the hypotenuse in a right triangle.

Cosine is the adjacent side divided by the hypotenuse in a right triangle.

Finding trigonometric values from one given trigonometric function

Given $\cos\phi=\frac{8}{10},\ find\ \cot\ and\ \csc\ \phi.$

First, find the missing side:

a^2+8^2=10^2

a^2=100-64

a^2=36

\sqrt{a^2}=\sqrt{36}

a=6

Find trigonometric values from one given trigonometric function

Remember, $a=6,\ b=8,\ and\ c=10$
$\cos\phi=\frac{8}{10},\ so\ \sin\phi=\frac{6}{10},\ and\ \tan\phi=\frac{6}{8}$ $\cot\phi=\frac{8}{6}$

Open Ended

$Given\ \sin\phi=\frac{8}{17},\$ find $\sec\phi\ and\ \tan\phi$

Type response here

Graph of tangent

The graph of tangent is increasing everywhere in its domain.
The period is $\pi$
It has asymptotes starting at $\frac{\pi}{2}$ and every $\frac{\pi+2x\pi}{2}where\ x=an\ integer.$

Open Ended

$What\ is\ the\ height\ of\ a\ building\ that\ cast\ a\ 40\ foot\ shadow\$ $when\ the\ earth\ is\ at\ a\ 60\degree\ to\ the\ sun?$ (Give an answer to the nearest foot)

Type response here

Error Analysis

Rodrigo was asked to identify the phase shift for the graph:

y=-\cos\left(\theta-\frac{\pi}{6}\right)-4

He\ said\ the\ the\ phase\ shift\ was\ \frac{\pi}{6}to\ the\ left

and 4 units down.
Is he correct?

Multiple Choice

What is $\cos\theta\ if\ \sin\theta=\frac{-9}{15}and\ \theta\ is\ in\ Quadrant\ IV$

$\cos\theta=\frac{9}{15}$

$\cos\theta=\frac{12}{15}$

$\cos\theta=\frac{-12}{15}$

$\cos\theta=\frac{-9}{15}$

Topic 7 Trigonometric Functions

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