Answer:
1. tan 35° = 0.700
2. sin 60° = 0.866
3. cos 25° = 0.906
4. tan 75° = 3.732
5. cos 45° = 0.707
6. sin 20° = 0.342
7. tan 80° = 5.671
8. cos 40° = 0.766
9. tan 55° = 1.428
10. sin 78° = 0.978
Step-by-step explanation:
Trigonometric ratios, also known as trigonometric functions, are mathematical ratios that describe the relationship between the angles of a right triangle and the ratios of the lengths of its sides. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
Rounding to three decimal places is a process of approximating a number to the nearest value with three digits after the decimal point. In this rounding method, the digit at the fourth decimal place is used to determine whether the preceding digit should be increased or kept unchanged.
To round a number to three decimal places, identify the digit at the fourth decimal place (the digit immediately after the third decimal place).
- If the digit at the fourth decimal place is 5 or greater, increase the digit at the third decimal place by 1.
- If the digit at the fourth decimal place less than 5, keep the digit at the third decimal place unchanged.
Finally, remove all the digits after the third decimal place.
Entering tan 32° into a calculator returns the number 0.7002075382...
To round this to three decimal places, first identify the digit at the fourth decimal place:
[tex]\sf 0.700\;\boxed{2}\;075382...\\ \phantom{w}\;\;\;\;\;\;\:\uparrow\\ 4th\;decimal\;place[/tex]
As this digit is less then 5, we do not change the digit at the third decimal place. Finally, remove all the digits after the third decimal place.
Therefore, tan 32° = 0.700 to three decimal places.
Apply this method to the rest of the given trigonometric functions:
- tan 35° = 0.7002075382... = 0.700
- sin 60° = 0.8660254037... = 0.866
- cos 25° = 0.9063077870... = 0.906
- tan 75° = 3.7320508075... = 3.732
- cos 45° = 0.7071067811... = 0.707
- sin 20° = 0.3420201433... = 0.342
- tan 80° = 5.6712818196... = 5.671
- cos 40° = 0.7660444431... = 0.766
- tan 55° = 1.4281480067... = 1.428
- sin 78° = 0.9781476007... = 0.978
