Home > Trigonometry > Half-Angle Identities

If cos(θ)=3/5, what is the value of sin(θ)?

Just a math question I don't get. Also, it is one of those questions where its "click all that apply" so there might be more then one answer I guess. Please and Thanks :)

Answer 1

Josiah Anderson

#+-4/5#

We have: #costheta=3/5#

By applying the identity of Pythagore,

#cos^2theta+sin^2theta=1#

So.

#9/25+sin^2theta=1#

#sin^2theta=1-9/25#

#=16/25#

#:.sintheta=sqrt(16/25)#

#=+-4/5#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Samantha Abate

The value is #4/5#

We know from the given that #cos(θ)= 3/5# So then to simplify further, we will divide: #cos(θ)= 3/5 rarr cos(θ) = 0.6# Since we want to find the value of θ, we have to use the inverse operation on the calculator. We want to figure out which angle (that has the value of θ in this example) resulted in a cosine of 0.6. #cos(θ) = 0.6# (hit #2nd# button then hit #cos# button) #θ ~~ 53.13#

Now that we know that value of θ, we are able to plug that in to the other equation. #sin(θ) = x rarr sin(53.13) = x# Now use the normal #sin# button on your calculator to find the value of #x# #sin(53.13) ~~ 0.8# or #4/5#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.