Question

Determine two other angles that have the same trigonometric function value: a) sin 47 b) cos 56. For a, the value is 0.731 and for b) it's 0.559?

Answer 1

a) 133 , b) 304

Sin and cos are periodic functions. The period is 2`pi` (360 degrees). During the interval 0 to 2`pi` they repeat the same value twice.

Also remember, sin has positive values in the 1st and 2nd quadrant
whereas cos has positive values in the 1st and the fourth quadrant.

Besides, if `pi` is added to any angle measure or an angle measure is subtracted from `pi`, the sin ratio remains sin and cos remains cos.

The given value for sin47 would therefore be repeated in the 2nd quadrant and this would be given by 180-47 = 133

The given value for cos would repeat itself in 4th quadrant and it would be 360-56 = 304.

Now go on adding 360 to 47 and 133, to get any number of angles having sin value 0.731. Similarly go on adding 360 to 56 and 304 to get any number of angles having cosine value 0.559