Prove the Pythagorean identity sin[math]^2\theta +[/math] cos[math]^2\theta = 1[/math].

[list=1] [*]Draw a labeled diagram of a right triangle. [*]Apply the Pythagorean Theorem to this triangle. [*]Divide both sides of this equation by [math]r^2[/math]. [*]Rewrite this equation using the laws of exponents. [*]Find sin [math]\theta[/math] and cos [math]\theta[/math] by looking at the diagram. [*]Substitute sin [math]\theta[/math] and cos [math]\theta[/math] into the equation from step 4. [*]Rewrite the equation using the standard notation for trigonometric functions with exponents. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway: Mathematics III[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

If sin [math]\theta = \frac{2}{5}[/math] and [math]0 < \theta < 90[/math], use the Pythagorean identity sin[math]^2\theta +[/math] cos[math]^2\theta = 1[/math] to find the values of cos [math]\theta[/math] and tan [math]\theta[/math].

[list=1] [*]Substitute the given value of sine into the identity. [*]Solve for cos [math]\theta[/math]. [*]To find tan [math]\theta[/math], use the ratio identity [math]\text{tan } \theta = \frac{\text{sin } \theta}{\text{cos } \theta}[/math]. [*]Summarize your findings. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway: Mathematics III[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.