Given secθ=1213, calculate all other trigonometric ratios

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Given sec: = {13}{12}, calculate all other trigonometric rat

Question

Given $sec θ = \frac{13}{12}$ , calculate all other trigonometric ratios

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Theodore Discussed

Given

sec θ = \frac{13}{12}

, calculate all other trigonometric ratios

11 mins ago

Discuss this question LIVE

11 mins ago

sec θ = \frac{13}{12} \Rightarrow cos θ = \frac{1}{sec θ} = \frac{12}{13}

sin θ = 1 - cos^{2} θ = 1 - (\frac{12}{13})^{2} = 1 - \frac{144}{169} = \frac{25}{169} = \pm \frac{5}{13}

Note

cos θ

is positive in first and fourth quadrant and

sin θ

is positive in first quadrant and negative in third quadrant.

csc θ = \frac{1}{sin θ} = \frac{1}{\frac{\pm 5}{13}} = \pm \frac{13}{5}

tan θ = \frac{sin θ}{cos θ} = \frac{\pm \frac{13}{5}}{\frac{12}{13}} = \frac{\pm 13}{12}

cot θ = \frac{1}{tan θ} = \pm \frac{12}{13}

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Question Text	Given $sec θ = \frac{13}{12}$ , calculate all other trigonometric ratios
Answer Type	Text solution:1
Upvotes	150