7.4 Trigonometry What you’ll learn: To find trig ratios using right triangles. To solve problems using trig ratios.

Trigonometry Trigonometry – the study of triangle measurement Trigonometric Ratio – the ratio of the lengths of sides of a right triangle. Three most common trig ratios – sine, cosine, and tangent. Trig ratios are related to the acute angles of a right triangle, never the right angle.

A B C a b c Sine ratio sin of A= or sin of B= or

Cosine Ratio A B C a b c cos of A= or cos of B= or

A B C a b c Tangent Ratio tan of A= or tan of B= or

Writing Ratios Find sin A, cos A, tan A, sin B, cos B, tan B. Express each ratio as a fraction and as a decimal to the nearest hundredth. sin A= cos A= tan A= sin B= cos B= tan B= A B C 15 8 17

Using the calculator Scientific calculators are programmed to know what the ratios will be for all angles. You can enter the angle and it will give you the ratio (as a decimal) or you can enter the ratio and it will give you the angle. Since we are dealing only with degrees, make sure your calculator is in “degree” mode (D or DEG should be visible) When you are given the angle: Example: sin 50 (enter sin 50 then press enter or enter 50 and press sin) 0.7660

When you are given the ratio: To find the angle from a ratio, you must use the “second” or “shift” key to find it. (use etc..) Ex: cos X=0.8734 Enter Shift cos 0.8734 then enter or 0.8734 and shift cos X=29.14

Finding Missing Parts. Find x to the nearest tenth. 1. 2. 3. 4. x 14 16 46 32 9 X 18 x 7.5 15

Homework p. 368 18-48 even