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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.

sinθ=45,θis acute.

Short Answer

Expert verified

The exact value of sinθ=45of the remaining trigonometric functions are,

role="math" localid="1646366252886" 1.cscθ=542.cosθ=353.secθ=534.tanθ=435.cotθ=34

Step by step solution

01

Step 1 Given expression is,

sinθ=45.

Let P=x,yis a point on the circle that corresponds to θ. Since sinθ=45>0and the angle θis acute , therefore the point Plies in the first quadrant.

02

Step 2 Let us consider y=4,r=5.

So, the point Px,4corresponds to θlies on the circle of radius 5.

x2+42=52x2+16=25x2=25-16x2=9x=±3

03

Step 3 Since Px,y lies in the first quadrant, we take y=4,x=3,r=5.

cscθ=ry=54cosθ=xr=35secθ=rx=53tanθ=yx=43cotθ=xy=34

These are the remaining trigonometric functions of the given expression.

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