Question

If secθ = 13\5 and 270° < θ < 360°, then tanθ = _____. -12\5 -5\12 5\12 12\5

Answer 1

Answer:

tanΘ = - $\frac{12}{5}$

Step-by-step explanation:

Using the trigonometric identity

tan²Θ + 1 = sec²Θ, thus

tan²Θ + 1 = ($\frac{13}{5}$ )² = $\frac{169}{25}$ ( subtract 1 from both sides )

tan²Θ = $\frac{144}{25}$ ( take the square root of both sides )

tanΘ = ± $\sqrt{\frac{144}{25} }$

Since 270 < Θ < 360 , that is the fourth quadrant where tan Θ < 0, thus

tanΘ = - $\frac{12}{5}$