Question

Sec 15π/4 find the value with steps

Answer 1

To find the value of sec 15π/4

We know that,

π=180

Firstly,find out the value of 15π/4

$\frac{15 \pi}{4} \\ \\ = \frac{15 \times 180}{4} \\ \\ = 15 \times 45 \\ \\ = 675$

Implies,

sec15π/4

=sec675

Now,

sec675 can also be expressed as sec[(2×360)+45]

Thus,

sec675

=sec45

From the trigonometric table,

sec 45 = √2

Answer 2

Answer:

Sec 15π/4 = $\sqrt{2}$

Step-by-step explanation:

We know that,

π = 180

Firstly,find out the value of 15π/4

15*180/4=675

⇒sec15π/4 = sec675

Now,

sec675 can also be expressed as sec(360 +315)

sec(360 +315) = sec(315)

                       = sec(360 -45)  {(360 - ∅) is in Q4 where cos and sec are                    

                                                                                                       positive}

sec(360 +315) = sec(360 -45)

sec(360 +315) = sec 45

sec(360 +315)   = $\sqrt{2}$   (From the trigonometric value table ,sec 45 = √2)

sec675 = $\sqrt{2}$

Therefore Sec 15π/4 = $\sqrt{2}$

similarly csc 15π/4 = -$\sqrt{2}$.