Unit 7 Lesson 7.2: Trigonometric Ratios

​Trigonometric Ratios

​Trigonometric Ratios

• Wh​en using trig functions, you must begin at an angle (do NOT use the 90° angle).

• If we look at angle Θ​, the opposite side sits ACROSS from it and the adjacent side is DIRECTLY NEXT TO it.

• The hypotenuse will ALWAYS stay the same. ​

​Trigonometric Ratios

​After you plug in the numbers for the ratios, you can use your calculator to simplify it to a decimal.

​Trigonometric Ratios

​Notice that since we switched to ∠B:

• The hypotenuse did not change.

• The opposite and adjacent sides swapped. ​

​Trigonometric Ratios

Key Points:

• sin A = cos B

• sin B = cos A

• tan A ×​ tan B = 1

​

These must ALWAYS be true, and you can use these to check that your work is correct!

When we can't use Pythagorean Theorem to calculate missing sides, we can use a trig ratio instead. ​

​Step 1: Determine which trig ratio you need.

Step 2: Set up the ratio using the pieces from the triangle.

Step 3: Solve for x. ​

Step 1: Determine which trig ratio you need.

To choose the right ratio, start at the angle (76°​).

• The side x lies OPPOSITE of 76°​.

• The side 6 ft lies ADJACENT to 76°​.

​

The ratio that uses OPPOSITE & ADJACENT is TANGENT. ​

Step 2: Set up the ratio using the pieces of the triangle.

Step 3: Solve for x.

Every function has an inverse (or "opposite"). The inverse of trigonometric ratios will actually help us calculate missing angles rather than missing sides.

​

​

​

Basically what happens is this: ​

​Inverse Trig Ratios:

Given ΔABC, find ∠A to the nearest whole degree.​

​

Step 1: Determine which trig ratio you need.

Step 2: Set up the ratio like normal.

Step 3: Switch the angle and the ratio.

Step 4: Solve for the missing angle. ​

Step 1: Determine which trig ratio you need. ​

​To choose the right ratio, start at ∠A:

• The side 19 in. is OPPOSITE of ∠​A.

• The side 36 in. is​ ADJACENT to ∠​A.

​

The ratio that uses OPPOSITE & ADJACENT is TANGENT. ​

Step 2: Set up the trig ratio like normal. ​

Step 3: Switch the angle and the ratio. ​

Step 4: Solve for the missing angle. ​

Step 4: Solve for the missing angle. ​