5-Minute checks YZ

7.6 Apply the sine and cosine ratios Students will recognize and apply the sine & cosine ratios where applicable. Why? So you can find distances, as seen in EX 39. Mastery is 80% or better on 5-minute checks and practice problems.

Trigonometric Ratios- concept develop Let ∆ABC be a right triangle. The since, the cosine, and the tangent of the acute angle A are defined as follows. Side adjacent to A b cos A = = hypotenuse c Side opposite A a sin A = = hypotenuse c Side opposite A a tan A = = Side adjacent to A b

Example 1 – skill develop

Think ….Ink….Share

Example 2 Finding the Cosine – skill develop

Example 3 -HOTS Think….Ink….Share

Example 3 Solutions

With A pARTNER

Example 4 – hots Finding a Hypotenuse using an angle of depression

Example 4 solution

Check for understanding

Example 5 Find leg length using angles of elevation- real world application

Example 5 solution

Example 5 solution

Example 6 using special right triangles –guided practice & apk

Example 6 continued

Think …..Ink….Share When looking for missing lengths & angle measures what is the determining factor in deciding to use Sin, Cos & Tan? How do you know which on to use?

What was the objective for today? Students will recognize and apply the sine & cosine ratios where applicable. Why? So you can find distances, as seen in EX 39. Mastery is 80% or better on 5-minute checks and practice problems.

Homework PDF Sine, Cos & Tan Review Work Sheet Online in the HW tab

Ex: 5 Using a Calculator You can use a calculator to approximate the sine, cosine, and the tangent of 74. Make sure that your calculator is in degree mode. The table shows some sample keystroke sequences accepted by most calculators.

Sample keystrokes Sample keystroke sequences Sample calculator display Rounded Approximation 74 0.961262695 0.9613 0.275637355 0.2756 3.487414444 3.4874 sin sin ENTER 74 COS COS ENTER 74 TAN TAN ENTER

Trigonometric Identities A trigonometric identity is an equation involving trigonometric ratios that is true for all acute triangles. You are asked to prove the following identities in Exercises 47 and 52. (sin A)2 + (cos A)2 = 1 sin A tan A = cos A