Question

Use the Special Right Triangle to evaluate sin 45°, cos 45° and tan 45°. Your answers should be exact (not a decimal).

A. sin 45 = √2/2, cos 45 = √2/2, tan 45 = 1
B. sin 45 = 1, cos 45 = 1, tan 45 = √2/2
C. sin 45 = 1/2, cos 45 = √3/2, tan 45 = √3
D. sin 45 = 0, cos 45 = 1, tan 45 = 0

Answer 1

The correct option is A)
`\sin 45^(\circ) =(√(2))/(2),\ \cos 45^(\circ) =(√(2))/(2) \ \text{and} \ \tan 45^(\circ) =1`

Explanation:

we need to evaluate
`\sin 45^(\circ), \ \cos 45^(\circ) \ \text{and} \ \tan45^(\circ)` with the use of special right triangle

In triangle ABC (figure -1 )

Since,
`\sin \theta =(opposite)/(hypoteneous)`

`\cos  \theta =(adjacent)/(hypoteneous)`

`\tan  \theta =(opposite)/(adjacent)`

so,

`\sin 45^(\circ) =(opposite)/(hypoteneous)`

`\sin 45^(\circ) =(x)/(x√(2))`

`\sin 45^(\circ) =(1)/(√(2))`

`\cos 45^(\circ) =(adjacent)/(hypoteneous)`

`\cos 45^(\circ) =(x)/(x√(2))`

`\cos 45^(\circ) =(1)/(√(2))`

and

`\tan  45^(\circ) =(opposite)/(adjacent)`

`\tan  45^(\circ) =(x)/(x)`

`\tan 45^(\circ) =1`

Therefore, the correct option is A)
`\sin 45^(\circ) =(√(2))/(2),\ \cos 45^(\circ) =(√(2))/(2) \ \text{and} \ \tan 45^(\circ) =1`

Answer 2

The best option is (A) sin 45 = √2/2, cos 45 = √2/2, tan 45 = 1.