Question

Draw a triangle whose cosine is 0.63. Then find the value of the other five trigonometric functions ​

Answer 1

Answer:

• sin = 0.776595
• tan = 1.23269
• sec = 1.58730
• csc = 1.28767
• cot = 0.811234

Step-by-step explanation:

Cosine is the name of a function of an angle, not a triangle. We have drawn a triangle containing an angle (α) whose cosine is 0.63.

The cosine is the ratio of the adjacent leg of a right triangle to the hypotenuse, where "adjacent" refers to the angle of interest. In our triangle, we have ensured the cosine is 0.63 by making the adjacent leg be 63 and the hypotenuse be 100.

The length of the opposite leg can be found from the Pythagorean theorem.

  opp = √(100² -63²) = √6031

The sine function is the ratio of that to the hypotenuse:

  sin(α) = (√6031)/100 ≈ 0.776595

The tangent function is the ratio of opposite to adjacent sides:

  tan(α) = (√6031)/63 ≈ 1.23269

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The secant is the inverse of the cosine:

  sec(α) = 1/0.63 ≈ 1.58730

The cosecant is the inverse of the sine:

  csc(α) = (100√6031)/6031 ≈ 1.28767

and the cotangent is the inverse of the tangen:

  cot(α) = (63√6031)/6031 ≈ 0.811234