1. What is Cos (pi/2+A)?

Cos (pi/2+A) represents the cosine of the sum of π/2 (90 degrees) and angle A. This trigonometric expression demonstrates the phase shift property of cosine function when combined with a right angle.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \( A \) — Angle in radians
• \( \pi/2 \) — 90 degrees in radians (approximately 1.5708)
• \( \sin \) — Sine trigonometric function

Explanation: This identity shows that cosine of an angle shifted by π/2 equals the negative sine of the original angle, demonstrating the complementary relationship between sine and cosine functions.

3. Trigonometric Identity Explanation

Details: This identity is derived from the angle addition formula for cosine: cos(x+y) = cos(x)cos(y) - sin(x)sin(y). When x = π/2 and y = A, we get cos(π/2+A) = cos(π/2)cos(A) - sin(π/2)sin(A) = 0·cos(A) - 1·sin(A) = -sin(A).

4. Using the Calculator

Tips: Enter the angle value in radians. The calculator will compute cos(π/2 + A) using the identity cos(π/2 + A) = -sin(A). For degrees, convert to radians first (degrees × π/180).

5. Frequently Asked Questions (FAQ)

Q1: Why does cos(π/2 + A) equal -sin(A)?
A: This results from the angle addition formula and the specific values of cos(π/2) = 0 and sin(π/2) = 1.

Q2: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180 (approximately 0.0174533).

Q3: What is the range of possible results?
A: Since sine function ranges from -1 to 1, the result will range from -1 to 1 (inclusive).

Q4: Are there similar identities for other trigonometric functions?
A: Yes, similar identities exist such as sin(π/2 + A) = cos(A) and tan(π/2 + A) = -cot(A).

Q5: When is this identity particularly useful?
A: This identity is useful in simplifying trigonometric expressions, solving equations, and in applications involving phase shifts in wave functions.