Start learning 50% faster. Sign in now
We are given: sin⁴x + cos⁴x = 5/8 We are asked to find the value of sin(2x). We use the identity: sin⁴x + cos⁴x = (sin²x + cos²x)² - 2sin²x·cos²x But sin²x + cos²x = 1, so: sin⁴x + cos⁴x = 1 - 2sin²x·cos²x We are given: 1 - 2sin²x·cos²x = 5/8 ⇒ 2sin²x·cos²x = 1 - 5/8 = 3/8 Now, recall: sin(2x) = 2sinx·cosx So: sin²(2x) = [2sinx·cosx]² = 4sin²x·cos²x From above, we found: sin²x·cos²x = 3/16 ⇒ sin²(2x) = 4 × 3/16 = 3/4 ⇒ sin(2x) = √(3/4) = √3 / 2
The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)
Find the area of largest square that can be inscribed in a circle of radius ‘r’.
In the given diagram, point 'O' represents the center of a circle, while AB and DE are two distinct chords within the circle. The line segment OC is per...
Find the area of the sector of a circle with radius 14 cm and central angle 90°.
A circle touches all four sides of a quadrilateral. If AB = 18 cm, BC = 21 cm, and AD = 15 cm, then what is the length of CD?
A sector of a circle has a central angle of 120° and a radius of 10 cm. Find the area of the sector.