Question

question 16 (1 point)
the point (-2, 5) is on the terminal arm of db.which is the set of exact primary trigonometric ratios for the angle?
o a)
5
2
sin b =
cos b = -
√29
√29
5
tan b = -
2
o b)
2
5
sin b = -
cos b =
√29
√29
5
tan b = -
2
o c)
√29
√29
sin b =
cos b = -
5
2
2
tan b = -
5
o d)
√29
√29
sin b = -
cos b =
2
5
2
tan b = -
5
page

Explanation:

Step1: Calculate the radius \( r \)

For a point \((x,y)=(-2,5)\) on the terminal arm of an angle, use the formula \( r=\sqrt{x^{2}+y^{2}} \).

$$ r=\sqrt{(-2)^{2}+5^{2}}=\sqrt{4 + 25}=\sqrt{29} $$

Step2: Find \(\sin B\), \(\cos B\), and \(\tan B\)

Use the definitions \(\sin B=\frac{y}{r}\), \(\cos B=\frac{x}{r}\), \(\tan B=\frac{y}{x}\)

• \(\sin B=\frac{5}{\sqrt{29}}\)
• \(\cos B=\frac{-2}{\sqrt{29}}\)
• \(\tan B=\frac{5}{-2}=-\frac{5}{2}\)

Answer:

A. \(\sin B=\frac{5}{\sqrt{29}},\cos B =-\frac{2}{\sqrt{29}},\tan B=-\frac{5}{2}\)