In the Math question: tanB=15/8 , secB<0 , What does the secB<0 mean?

Question

In the Math question: tanB=15/8 , secB<0 , What does the secB<0 mean?

How can I find the other values using tanB=15/8? Where secB<0.

Answer 1

sec B < 0 is equivalent to cos B < 0.
As tan B > 0, this means the angle is in the 3rd quadrant.

Answer 2

there are 4 quadrants as below


0 to 90 degrees - 1st quadrant
90 to 180 degrees - 2nd quadrant
180 to 270 degrees - 3rd quadrant
270 to 360 degrees - 4th quadrant


( note: [multiples of 360] + or - angle = angle )


now trigonometric functions are +ve in some quadrants & -ve in some & u can remember that by following mnemonic

All Silver Tea Cups

1st quadrant A(all) -> all are +ve
2nd quadrant S(silver) - sin (& cosec) are +ve
3rd quadrant T(tea) - tan & (cot) are +ve
4th quadrant C(cups) - cos( & sec) are + ve

thus in ur case secB<0 implies B is in 2nd quadrant or 3rd quadrant

Answer 3

sec B is the reciprocal of cos B, so it's the same as telling you that cos B is negative.
That happens in the second and third quadrants. Of these, it's only in the third that tan B is positive, so if you're asked to find, say, sin B or cosec B (reciprocal of sin B), knowing the angle is in the third quadrant you give the sine a negative value (actually it's -15/17)

Answer 4

secB = 1/cosB. Remember, tanB = sinB/cosB
so, cosB = +/-8. and secB = 1/cosB, so secB = +/- 1/8

but you want where secB < 0, so secB = - 1/8