Question

evaluate sec 1020 degree​

Answer 1

Answer:

May be sec 1020 is 2.

Step-by-step explanation:

Reciprocal of 1/ cos 1020 = sec 1020 = 2

Answer 2

$\sec 1020$° = 2

Step-by-step explanation:

We have,

$\sec 1020$°  

To find, the value of $\sec 1020$° = ?

We know that,

180° = $\pi^c$

1020° = $(\dfrac{\pi}{180} \times 1020)^c$

= $(\dfrac{\pi}{18} \times 102)^c$

Dividing numerator and denominator by 6, we get

= $(\dfrac{17\pi}{3})^c$

∴ $\sec 1020$° = $\sec (\dfrac{17\pi}{3})$

= $\sec (6\pi-\dfrac{\pi}{3})$

Using the trigonometric identity,

$\sec (2\pi-x)$ = $\sec x$

= $\sec \dfrac{\pi}{3}$

= $\sec 60$° [∵ $\sec 60$° = 2]

= 2

∴ $\sec 1020$° = 2

Thus, the value of $\sec 1020$° = 2