What is the value of cos 75°?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The value of cos 75° is (√3-1) / 2√2. Trigonometric functions are mathematical functions that relate angles in a right triangle to the ratios of the sides of that triangle. These functions help us understand and analyze the relationships between angles and sides in trigonometry.
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Value of cos 75°
The six primary trigonometric functions are Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), and Cosecant (cosec). These trigonometric functions are widely used in various fields, such as mathematics, physics, engineering, and navigation, to solve problems involving angles and triangles.
Solution:
We can express 75° as the sum of two angles: 75° = 30° + 45°.
Using the formula for cos(A + B) = cos(A)cos(B) – sin(A)sin(B), we can find the value of cos 75°.
cos(75°) = cos(30° + 45°)
Now, we know that cos 30° = √3/2, cos 45° = √2/2, sin 30° = 1/2, and sin 45° = √2/2 from the special values of trigonometric functions.
cos(75°) = cos(30°)cos(45°) – sin(30°)sin(45°)
Substituting the known values:
cos(75°) = (√3)/2)(√2)/2) – (1/2)(√2)/2)
Simplifying:
cos(75°) = (√6)/4) – (√2)/4)
Combining the terms:
cos(75°) = (√6 – √2))/4 = (√3-1) / 2√2
Therefore, cos 75° is equal to (√3-1) / 2√2 or 0.2588.
Summary:
What is the value of cos 75°?
(√3-1) / 2√2 is the value of cos 75°. Moreover, cos 75° can be written as 0.2588 or (√3-1) / 2√2.
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