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3 years ago

Find the exact values of the sine, cosine, and tangent of the angle. 255=300-45

1 answer:

7 0

Sin 255 = sin(300 - 45) = sin 300 cos 45 - cos 300 sin 45; where sin 300 = -sin(360 - 60) = - sin 60 = -√3/2, sin 45 = cos 45 = 1/√2, cos 300 = cos(360 - 60) = cos 60 = 1/2
Therefore, sin 255 = (-√3/2)(1/√2) - (1/2)(1/√2) = -√3/2√2 - 1/2√2 = -(√3 + 1)/2√2 = -(√6 + √2)/4

cos 255 = cos(300 - 45) = cos 300 cos 45 + sin 300 sin 45 = (1/2)(1/√2) + (-√3/2)(1/√2) = (1 - √3)/2√2 = (√2 - √6)/4

tan 255 = tan(300 - 45) = (tan 300 - tan 45)/(1 + tan 300 tan 45); where tan 300 = sin 300 / cos 300 = (-√3/2) / (1/2) = -√3 and tan 45 = 1
Therefore, tan 255 = (-√3 - 1)/(1 + (-√3)) = (-√3 - 1)/(1 - √3) = √3 + 2

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Solve for x: -3x + 3< 6

Katarina [22]

Answer:

x > -1

Step-by-step explanation:

-3x + 3< 6
-3x < 3
x > -1
Hope it helped !
Adriel

8 0

3 years ago

Read 2 more answers

let t : r2 →r2 be the linear transformation that reflects vectors over the y−axis. a) geometrically (that is without computing a

tangare [24]

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

See the figure for the graph:

(a) for any (x, y) ∈ R² the reflection of (x, y) over the y - axis is ( -x, y )

∴ x → -x hence '-1' is the eigen value.

∴ y → y hence '1' is the eigen value.

also, ( 1, 0 ) → -1 ( 1, 0 ) so ( 1, 0 ) is the eigen vector for '-1'.

( 0, 1 ) → 1 ( 0, 1 ) so ( 0, 1 ) is the eigen vector for '1'.

(b) ∵ T(x, y) = (-x, y)

T(x) = -x = (-1)(x) + 0(y)

T(y) = y = 0(x) + 1(y)

Matrix Representation of $T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$

now, eigen value of 'T'

$T - kI = \left[\begin{array}{cc}-1-k&0\\0&1-k\end{array}\right]$

after solving the determinant,

we get two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Hence,

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Learn more about " Matrix and Eigen Values, Vector " from here: brainly.com/question/13050052

#SPJ4

6 0

1 year ago

A definite integral of f(x)dx on the interval a to b probably SHOULDN'T be used:

OLga [1]

= cos( -x ) * [ - sin( - x ) ] = cosx * sinx ;
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3 years ago

A cheetah can travel three hours at top speed for 225 miles how many miles per hour?

jolli1 [7]

Answer:

The answer is 75 miles per hour

Step-by-step explanation:

225÷3=75 ( how many times 3 go into 225)

We can check to see if this answer is correct by multiplying 75 by 3 ( multiply 75 three times)

75×3=225

There for 75 is the correct answer

(I hope this helped you answer your question. If you want to check if I'm correct you can use a calculator! Have a wonderful day!)

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3 years ago

A __ fraction is a fraction whose denominator is 10,100,or some other multiple of 10.

Alexxandr [17]

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Step-by-step explanation:

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3 years ago