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# 8 Finding angles from trigonometric ratios

Inverse trigonometric values can be found using the second functions , and of the , and keys. These functions are used in a similar manner to , and .

## Activity 17 Finding angles from trigonometric ratios

Calculate the value of each of the following expressions using your calculator, where possible, giving your answers correct to 1 decimal place.

### Answer

1. .

   If you obtained the answer or 0.5236 (to 4 decimal places), then your calculator is set to work in radians. Make sure that you are working in degrees.

2. (to 1 decimal place).
3. (to 1 decimal place).
4. The calculation is not possible, and your calculator will give a ‘Math Error’. There is no angle whose sine is 2, because the hypotenuse is always the largest side of a right-angled triangle, and hence the maximum value the sine of an angle can be is 1.

In part (1) of the activity above, you used your calculator to find an angle whose sine is 0.5. This is not the only angle whose sine is 0.5, but you can use this angle to find the other angles. Similar remarks apply to parts (2) and (3).

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