Question

the value of sin 37 degree sec 53 degree is

Answer 1

Answer:

The value of sin 37° sec 53° is approximately 0.7489.

Step-by-step explanation:

To find the value of sin 37 degrees sec 53 degrees, we can start by using the trigonometric identity that relates secant and cosine:

$\sec( θ ) = \frac{1}{ \cos( θ ) }$

Substituting 53 degrees for θ, we get:

$\sec( 53 ) = \frac{1}{ \cos( 53 ) }$

Next, we can use the identity that relates sine and cosine:

${ \sin^{2} ( θ) } + { \ { \cos }^{2} (θ) } = 1$

Solving for cosine, we get:

$\cos(θ) = \sqrt{1 - { \sin}^{2}θ }$

Substituting 37 degrees for θ, we get:

$\cos(37) = \sqrt{1 - { \sin }^{2}37 }$

Now, we can substitute both of these expressions into the original equation:

$\sin(37) \sec(53) = \sin(37) \frac{1}{ \cos(53) }$

$= \frac{ \sin(37) }{ \cos(53) }$

$= \frac{ \sin(37) }{ \sqrt{1 - { \sin }^{2}37 } }$

We can use a calculator or trigonometric tables to find that sin 37 degrees is approximately 0.6018. Substituting this value, we get:

$\sin(37) \sec(53) = \frac{0.6018}{ \sqrt{1 - {0.6018}^{2} } }$

$\frac{0.6018}{ \sqrt{0.6374} }$

= 0.7489 (rounded to four decimal places)

Therefore, the value of sin 37 degrees sec 53 degrees is approximately 0.7489.

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Answer 2

sin 37° × sec 53° = 1

Correct question : Find the value of sin 37° × sec 53°

Given :

The expression sin 37° × sec 53°

To find :

The value of the expression

Formula Used :

sin (90° - θ) = cos θ

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is sin 37° × sec 53°

Step 2 of 2 :

Find the value of the expression

We are aware of the formula that

sin (90° - θ) = cos θ

Thus we get

sin 37° × sec 53°

= sin (90° - 53°) × sec 53°

= cos 53° × sec 53°

= cos 53° × 1/cos 53°

= 1

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