Question

Q 1 PLEASE HELP ME FIGURE THIS OUT

Answer 1

Explanation:

tan is opposite over adjacent which gives you the side lengths. Use Pythagorean Theorem to find the hypotenuse. 1² + 3² = c² ⇒ √10 = c

opposite = 1, adjacent = 3, hypotenuse = √10

Answers:

sin =
`(opposite)/(hypotenuse) = (1)/(√(10)) *(√(10) )/(√(10) ) =(√(10) )/(10)`

cos =
`(adjacent)/(hypotenuse) = (3)/(√(10)) *(√(10) )/(√(10) ) =(3√(10) )/(10)`

csc =
`(hypotenuse)/(opposite) = (√(10))/(1) =√(10)`

sec =
`(hypotenuse)/(adjacent) = (√(10))/(3)`

cot =
`(adjacent)/(opposite) = (3)/(1) = 3`

*****************************************************************************************

Explanation:

The graph provides the adjacent side and hypotenuse. Use Pythagorean Theorem to find the opposite side. (√15)² + b² = (2√5)² ⇒ b = √5

opposite = √5, adjacent = √15, hypotenuse = 2√5

Answers:

sin =
`(opposite)/(hypotenuse) = (√(5))/(2√(5)) =(1)/(2)`

cos =
`(adjacent)/(hypotenuse) = (√(15))/(2√(5)) =(√(3) )/(2)`

tan =
`(opposite)/(adjacent) = (√(5))/(√(15))= (1)/(√(3)) *(√(3) )/(√(3)) =(√(3) )/(3)`

csc =
`(hypotenuse)/(opposite) = (2√(5))/(√(5)) =2`

sec =
`(hypotenuse)/(adjacent) = (2√(5))/(√(15))= (2)/(√(3))*(√(3) )/(√(3))=(2√(3))/(3)`

cot =
`(adjacent)/(opposite) = (√(15))/(√(5)) = √(3)`

*****************************************************************************************

sec
`\frac{4\pi} {11}`

= cos
`(11)/(4\pi)`

= cos 1.14

= 0.9998