sin 30° and cos 30° = 2
A. True
B. False
Answer (2)
Calculate sin 30° which equals 0.5.
Calculate cos 30° which approximately equals 0.866.
Add sin 30° and cos 30°: 0.5 + 0.866 = 1.366 .
Since 1.366 = 2 , the statement is false: F a l se .
Explanation
Problem Analysis We need to determine if the statement 'sin 30° + cos 30° = 2' is true or false. First, let's find the values of sin 30° and cos 30°.
Calculate sin 30° The value of sin 30° is 0.5. This is because in a 30-60-90 triangle, the side opposite the 30° angle is half the length of the hypotenuse. Therefore, sin 30° = 2 1 = 0.5
Calculate cos 30° The value of cos 30° is approximately 0.866. This is because in a 30-60-90 triangle, the side adjacent to the 30° angle is 2 3 times the length of the hypotenuse. Therefore, cos 30° = 2 3 ≈ 0.866
Add sin 30° and cos 30° Now, let's add the values of sin 30° and cos 30°: s in 30° + cos 30° = 0.5 + 0.866 = 1.366
Compare the sum with 2 Since 1.366 is not equal to 2, the statement 'sin 30° + cos 30° = 2' is false.
Final Answer The statement is false. Therefore, the answer is B.
Examples
Understanding trigonometric values like sin 30° and cos 30° is crucial in fields like engineering and architecture. For example, when designing a ramp, engineers use these values to calculate the slope and angle of inclination needed for the ramp to meet accessibility standards. Similarly, architects use trigonometric functions to determine the angles and lengths of roof supports, ensuring structural stability.
The statement 'sin 30° + cos 30° = 2' is false because sin 30° equals 0.5 and cos 30° equals approximately 0.866, which add up to 1.366. Therefore, the answer is B. False.
;
