Trigonometry Unit 1

1-4 Trigonometric Functions of any Angle

Evaluating Trig Functions Example<br/><a href="https://expl.ai/EZTNAGZ">https://expl.ai/EZTNAGZ</a>

Need a video? <br>Watch this one from Khan Academy.

Using the Pythagorean trig identity

1-2 Right Triangle Trigonometry

Use this Geogebra Link to help you understand degree and radian measures.

Degrees vs Radians – GeoGebra Materials

1-2 Right Triangle Trigonometry.pdf

Day 2 of Right Triangle Trig- 1.2B Worksheet

1-2B Right Triangle Trig Word Problems.pdf

Here is a video you can watch for more information.

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What are the Trigonometric Reciprocal Identities? | Virtual Nerd

Coterminal Angles Action!!!  - GeoGebra

<strong>Positive</strong> angles are generated by counterclockwise rotation.<br/><strong>Negative</strong> angles are generated by clockwise rotation.<br/>Angles that have the same initial sides and terminal sides are called <strong>coterminal</strong>.

Example:  Determine Positive and Negative Coterminal Angles

The angular speed is the rate at which the thing turns, described in units like revolutions per minute, degrees per second, radians per hour, etc. <br/><br/>The linear speed is the speed at which a a point on the edge of the object travels in its circular path around the center of the object. The units can be any usual speed units: meters per second, miles per hour, etc.

On the unit circle, the radius is 1. Use this formula for circles of any given size.

1-4 Exercises_ Trig functions of any angle.pdf

1-3A Master Unit Circle Charts (1).pdf

1-3_ Unit Circle Problem Set.pdf

Do these Khan Academy practice problems before taking the JKI on the Unit Circle.

Unit circle

Unit circle (with radians)

On the unit circles, each point (x, y) can be designated (cos t, sin t).

Add these points to your master unit circle worksheet. What are the coordinate points for each of these t-values? 

Right Triangle Khan Academy Practice:<br/>Make sure you log in to your Khan Academy Account to receive credit.

Trigonometric ratios in right triangles

Right triangle word problems

Solve for a side in right triangles

Reciprocal trig ratios

If you forgot the special right triangle rules, you should review them before we start the unit circle.

Solve for an angle in right triangles

Special right triangles

<strong>Definition of Reference Angle </strong><br/>Let 𝜃 be an angle in standard position. Its reference angle is the acute angle 𝜃' formed by the terminal side of 𝜃 and the <strong>horizontal axis.</strong>

Do these Khan Academy Assignments if you need more practice.

Radians & arc length

Radians & degrees

1-1 Notes: Radian and Degree Measure

The starting position is the <strong>initial side</strong> of the angle, and the position after rotation is the <strong>terminal side.</strong>

The <em>domain</em> of the sine and cosine functions is the set of all real numbers, ℝ.<br/><br/><br/>To determine the <em>range</em> of these two functions, consider the unit circle. Because <em>r</em>&nbsp;=&nbsp;1, it follows that sin <em>t</em> = <em>y</em>, and cos <em>t</em> = <em>x</em>. Also, (<em>x</em>, <em>y</em>) is on the unit circle and you know that ﹣1 ≤ <em>y</em> ≤ 1, and ﹣1&nbsp;≤&nbsp;<em>x</em>&nbsp;≤&nbsp;1. So the values of the sine and cosine also range between ﹣1 and 1.

<strong>Definition of Radian</strong><br/><br/>One <strong>radian</strong> is the measure of a central angle 𝜃 that intercepts an arc <em>s</em> equal in length to the radius of the circle.

1-1 Radian and degree measure

Watch this video if you need more information about cofunction identities.

Sine & cosine of complementary angles

Adding 2𝜋 to each value of <em>t</em> in the interval [0, 2𝜋] completes a second revolution around the unit circle, leaving you in the same position (this is the same concept as coterminal angles).

<strong><em>Period</em></strong> of the sine and cosine functions is <strong>2𝜋</strong>

sin(<em>t</em> + 2𝜋<em>n</em>) = sin <em>t</em><br/>and <br/>cos(<em>t</em> + 2𝜋<em>n</em>) = cos <em>t</em><br/>for any integer <em>n</em> and real number <em>t</em>.

The cosine and secant functions are <em>even</em>.<br/>cos(⁻<em>t</em>) = cos <em>t</em>sec(⁻<em>t</em>) = sec <em>t</em><br/><br/>The sine, cosecant, tangent, and cotangent functions are <em>odd</em>.<br/><br/>sin(⁻<em>t</em>) = ⁻sin <em>t</em>csc(⁻<em>t</em>) = ⁻csc <em>t</em><br/>tan(⁻<em>t</em>) = ⁻tan <em>t</em>cot(⁻<em>t</em>) = ⁻cot&nbsp;<em>t</em>

Learning the Unit Cirlce.<br/><br/>You will take a JKI. This link can be used to help you memorize the values on the unit circle.

Unit Circle with Reference Triangles

1-3 Notes: The Unit Circle

Our first introduction to trigonometric functions is based on the unit circle. Its equation is given by

Label these points on your master unit circle paper. If you misssed class or you want an extra copy to practice, look on page 26.

Name

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