How do you solve 3sin2AtanA=2 for 0<A<180?

The first step in solving any trigonometric equation is to convert everything into sine and cosine functions. So in this case we need to start by converting the tanA. We can use the identity: tanA=sinA/cosA

Hence the equation becomes:

3sin2A x sinA/cosA=2

Next we need to deal with the double angle that we have in sin2A. This time we can use the double angle rule for sine which says: sin2A=2sinAcosA. We substitute this into our equation to get:

3 x 2sinAcosA x sinA/cosA=2

We can now simplify the equation by cancelling out cosA and combining sinA:


which we simplify further to:


square rooting both sides we get:


hence by taking the inverse of sine we get:

A=35.27 degrees

However this is only one possible solution. We need to use the general solution of sine to find all possible answers within the given angle range.

The general solution for sine is:

sin-1​=A +360k or 180-A +360k where k is an integer

Hence our answer becomes:

A= (35.27 or  144.73) +360k

but since only 35.27 and 144.73 lie in the given range of 0

A=35.27 or 144.73

Sarah W. A Level Maths tutor, GCSE Maths tutor, A Level Chemistry tut...

5 months ago

Answered by Sarah, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Sahil M.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered: Maths, Spanish+ 3 more

-Medical School Preparation-

“Hello! My name is Sahil and I am currently a medical student at the University of Manchester. I am really looking forward to tutoring you in Spanish, Chemistry, Biology or Maths as well as trying to help you during the difficult proce...”

£20 /hr

Juris B.

Degree: Computer Science (Bachelors) - St. Andrews University

Subjects offered: Maths, Computing


“I am a Computer Science at the University of St. Andrews. Before that however, I was a pupil in a school in the North-East of Scotland. With the combined passion and availability of superb teachers - I was given an opportunity to exce...”

£20 /hr

Felix H.

Degree: Aerospace Engineering (Bachelors) - Manchester University

Subjects offered: Maths


“I'm an Aerospace student at the University of Manchester. I've had a long standing love of my field, and, and I'mexcited to get people to perform at their best level in exams. The Tutorials Before getting into regular sessions, where ...”

MyTutor guarantee

About the author

Sarah W.

Currently unavailable: for new students

Degree: Robotics (Masters) - Bristol University

Subjects offered: Maths, Physics+ 3 more


“About Me: I am currently a Masters student in Robotics at the University of Bristol. My choice of degree was based on my love for hands on science. I will try to pass on this love to you during my tutorials! I have alot of experience...”

You may also like...

Posts by Sarah

How could I write a program to convert Km/h to m/s in python

How do you solve 3sin2AtanA=2 for 0<A<180?

In the presence of ultraviolet light, ethane and chlorine react to give a mixture of products. What are the products of this reaction?

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together. What is the speed of the trucks after the collision?

Other A Level Maths questions

How do you integrate xcos(x)?

What is a logarithm?

A curve has parametric equations x = 2 sin θ, y = cos 2θ. Find y in terms of x

Simple binomial: (1+0.5x)^4

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss