Geometry and TrigonometryVery hardComplementary angles inside sine and cosine
Geometry and Trigonometry practice question
For an acute angle with measure x°, sin(x°) = cos((2x − 15)°). What is the value of x?
Answer: 35
sin θ = cos φ when the two angles are complementary: θ + φ = 90. So x + (2x − 15) = 90, giving 3x = 105 and x = 35. Check: sin 35° = cos 55°, and 2(35) − 15 = 55.
Common wrong answers
- If you answered 15
- 15 sets the two angles EQUAL (x = 2x − 15). Sine equals cosine for complementary angles, not equal ones.
- If you answered 25
- 25 comes from x + 2x − 15 = 60 or another slip; the angles add to 90.
- If you answered 105
- 105 is 3x. Divide by 3.
More Geometry and Trigonometry questions
- Very hard
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is N… - Very hard
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the valu… - Very hard
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Very hard
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Very hard
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this c… - Very hard
What is the perimeter of triangle ABC?
Not affiliated with the College Board. SAT is a trademark of the College Board.