Find sine, sec0, and tane, where 0 is the angle shown in the figure.
Give exact values, not decimal approximations.
5
3
sin 0
sece
tan e
= 0

Find sine sec0 and tane where 0 is the angle shown in the figureGive exact values not decimal approximations53sin 0secetan e 0 class=


Answer :

Answer:

  [tex]\sin(\theta)=\dfrac{3\sqrt{34}}{34}\\\\\sec(\theta)=\dfrac{\sqrt{34}}{5}\\\\\tan(\theta)=\dfrac{3}{5}[/tex]

Step-by-step explanation:

You want the sine, secant, and tangent of the angle θ in a right triangle with opposite side 3 and adjacent side 5.

Hypotenuse

The length of the hypotenuse is found using the Pythagorean theorem.

  c² = a² +b² . . . . . . where a, b are the legs of the triangle

  c² = 5² +3² = 25 +9 = 34

  c = √34 . . . . . . . . the length of the hypotenuse

Trig functions

You are reminded how to find the trig functions by SOH CAH TOA. This is intended to help you remember ...

  Sin = Opposite/Hypotenuse
  Cos = Adjacent/Hypotenuse
  Tan = Opposite/Adjacent

You need to remember also that the secant is the reciprocal of the cosine, so ...

  Sec = Hypotenuse/Adjacent

Using the measures ...

  • Opposite = 3
  • Adjacent = 5
  • Hypotenuse = √34

these ratios are ...

  [tex]\boxed{\begin{array}{l}\sin(\theta)=\dfrac{3\sqrt{34}}{34}\\\\\sec(\theta)=\dfrac{\sqrt{34}}{5}\\\\\tan(\theta)=\dfrac{3}{5}\end{array}}[/tex]

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Additional comment

The sine is O/H = 3/√34. The denominator is rationalized by multiplying this fraction by (√34)/(√34) to give the value shown above.