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SinA CosA Formula

SinA CosA is the product of trigonometric functions sine and cosine. We know the trigonometric identity of sin2A which is given by, sin2A = 2 sinA cosA. So, we can use this formula to derive the formula of sinA cosA. This formula can be written as sinA cosA = sin2A / 2. We can use this formula to simplify and solve various problems in trigonometry. This formula is also used to find the value of the product of sine and cosine functions for half angles.

We can write the sinA cosA formula in terms of the tangent function. In this article, let us explore the sinA cosA formula and its applications. We will derive its formula in terms of sine and tangent functions and solve a few examples to understand its applications.

1. What is SinA CosA?
2. SinA CosA Formula
3. Derivation of SinA CosA Formula in Terms of Tan
4. Application of SinA CosA Formula
5. FAQs on SinA CosA Formula

What is SinA CosA?

SinA CosA is a formula in trigonometry that is used to solve various math problems. We use the sin2A formula to derive the formula for sinA cosA. It is equal to half of sin2A. We can express the sinA cosA in terms of tangent function as well. We have sin2A = 2 sinA cosA. So,

sin2A = 2 sinA cosA

⇒ sinA cosA = sin2A / 2

Hence, the sinA cosA is equal to half of sin2A.

SinA CosA Formula

As discussed above, the formula for sinA cosA is given by,

sinA cosA = sin2A / 2

We can write this formula in terms of tangent function as,

sinA cosA = tanA / (1 + tan2A)

We can use this sinA cosA formula to solve various trigonometry problems.

sinA cosA

Derivation of SinA CosA Formula in Terms of Tan

Now that we know the formula of sinA cosA in terms of sine function, we will use the formula of sin2A in terms of tan to derive the sinA cosA formula in terms of the tangent function. We know that sin2A = 2tanA / (1 + tan2A). So, we have

sinA cosA = sin2A / 2

= [2tanA / (1 + tan2A)] / 2

= tanA / (1 + tan2A)

Hence, the formula for sinA cosA in terms of tan is given by, sinA cosA = tanA / (1 + tan2A).

Application of SinA CosA Formula

We have understood the formula for sinA cosA, in this section we will solve a few examples using the formula to understand its application.

Example 1: Evaluate the value of sin30° cos30° using sinA cosA formula.

Solution: The formula for sinA cosA is given by, sinA cosA = sin2A / 2.

If A = 30°, then 2A = 60°. We know sin 60° = √3/2 using the trigonometry table. So, we have

sin30° cos30° = sin60° / 2

= (√3/2) / 2

= √3 / 4

Answer: sin30° cos30° = √3/4

Example 2: Find the value of sinA cosA if sin2A = 2/3

Solution: Using the sinA cosA formula, we have

sinA cosA = sin2A / 2

= (2/3) / 2

= 2/6

= 1/3

Answer: The value of sinA cosA if sin2A = 2/3 is equal to 1/3.

 

SinA CosA Examples

  1. Example 1: Find the value of sinA cosA if angle A = 45 degrees.

    Solution: We know that sin45° = 1/√2, cos45° = 1/√2

    So, sinA cosA = sin45° cos45°

    = 1/√2 × 1/√2

    = 1/2

    Answer: The value of sinA cosA if angle A = 45 degrees is equal to 1/2.

  2. Example 2: Find the integral of sin x cos x using sinA cosA formula.

    Solution: To find the integral of sin x cos x using the sinA cosA formula, we have sinA cosA = sin2A / 2.

    ∫sin x cos x dx = ∫(sin2x / 2) dx

    = ∫(1/2) sin 2x dx

    = (1/2) ∫ sin2x dx

    = (1/2) (-cos2x) + C

    = (-1/2) cos2x + C, where C is the integration constant

    Answer: Integral of sin x cos x is (-1/2) cos2x + C.

  3. Example 3: Calculate the value of sin15° cos15° using sinA cosA formula.

    Solution: The formula for sinA cosA is given by, sinA cosA = sin2A / 2.

    If A = 15°, then 2A = 30°. We know sin 30° = 1/2 using the trigonometry table. So, we have

    sin15° cos15° = sin30° / 2

    = (1/2) / 2

    = 1 / 4

    Answer: sin15° cos15° = 1/4

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FAQs on SinA CosA Formula

What is SinA CosA in Trigonometry?

SinA CosA is equal to half of sin2A. It is equal to the product of sine function and cosine function. SinA CosA formula can be determined using the sin2A formula.

What is SinA CosA Formula?

The sinA cosA formula is given by, sinA cosA = sin2A / 2. This formula is used to solve various trigonometry problems and find the values of the product of sine and cosine for angle A.

How to Use SinA CosA Formula?

We can use the sinA cosA formula to find the product of sine and cosine function for angle A. Simply, substitute the double angle 2A into the formula sinA cosA = sin2A / 2 to find the value of sinA cosA.

How to Derive SinA CosA Formula?

We can derive the sinA cosA formula using the sin2A formula. We have

sin2A = 2 sinA cosA

⇒ sinA cosA = sin2A / 2

What is SinA CosA Formula in Terms of Tan?

The sinA cosA formula in terms of tan is given by, sinA cosA = tanA / (1 + tan2A). This formula can be determined by substituting the sin2A formula in terms of tan into the formula sinA cosA = sin2A / 2.

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