Find the Other Trig Values in Quadrant I cos(x)=4/7

Problem

cos(x)=4/7, Quadrant I

Solution

1. Identify the given values for the right triangle. Since cos(x)=adjacent/hypotenuse let the adjacent side a=4 and the hypotenuse c=7

2. Apply the Pythagorean theorem to find the opposite side b In Quadrant I, all trigonometric values are positive, so b will be the positive square root.

a2+b2=c2

4+b2=7

16+b2=49

b2=33

b=√(,33)

3. Determine the sine value using the ratio sin(x)=opposite/hypotenuse

sin(x)=√(,33)/7

4. Determine the tangent value using the ratio tan(x)=opposite/adjacent

tan(x)=√(,33)/4

5. Determine the cosecant value by taking the reciprocal of the sine.

csc(x)=7/√(,33)

csc(x)=(7√(,33))/33

6. Determine the secant value by taking the reciprocal of the cosine.

sec(x)=7/4

7. Determine the cotangent value by taking the reciprocal of the tangent.

cot(x)=4/√(,33)

cot(x)=(4√(,33))/33

Final Answer

sin(x)=√(,33)/7,tan(x)=√(,33)/4,csc(x)=(7√(,33))/33,sec(x)=7/4,cot(x)=(4√(,33))/33

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