MYTUTOR SUBJECT ANSWERS

812 views

Solve the equation tanx/cosx = 1 for 0°<x<360°

Firstly we need to rearrange this equation so that it contains only one trigonometric function of x (i.e. tanx, cosx or sinx) which will make it much easier to solve.

We can do this in the following way:

First multiply both sides by cosx in order to get tanx = cosx.
It then helps to write tanx in terms of cosx and sinx (tanx = sinx/cosx) and if we put this into the equation we now have, we get sinx/cosx = cosx.
Then multiply both sides by cosx a second time, to get sinx=cos2x.
Now we know from rearranging the identity sin2x + cos2x = 1, that cos2x=1-sin2x, and so if we substitute this into our equation we get sinx=1-sin2 x.
This gives us sin2x+sinx-1=0, which gives an equation recognisable as a quadratic equation, all in terms of sinx, meaning it will now be far easier to solve.

To solve:

Trigonometric quadratic equations can sometimes look much more complicated to solve that a quadratic in the form ax2+bx+c=0 but they are really no different and just take some getting used to. In this case, instead of x coefficients, we have sinx coefficients, meaning our equation is in the form a(sinx)2+b(sinx)+c=0.

Like any other quadratic equation we can use the quadratic formula where a=1, b=1 and c=-1, which gives us the solutions sinx=(-1+sqrt5)/2 and sinx=(1+sqrt5)/2.

We then have to go back to the question and see that we are looking for solutions where x is between 0° and 360°. The clearest way to see where our solutions are is to draw the graph y=sinx with x axis from 0° to 360° and see for which values of x, y=(-1+sqrt5)/2 and for which values y=(1+sqrt5)/2.  We can immediately see that (1+sqrt5)/2 > 1 so there is no solution to sinx=(1+sqrt5)/2 because sinx is bounded above by 1 (i.e. can’t any value higher than 1)

To get the specific values for x where sinx=(-1+squrt5)/2, we can use arctan in the calculator, and then check from the graph we have drawn whether there are any other solutions in the domain.

If we do this, we see that x=38.2° and x=142° are the solutions to sinx=(-1+sqrt5)/2  in the domain.

So our solutions are x=38.2° and x=142° (rounded to 3sig.figures)

Linetta A. A Level Philosophy and Ethics tutor, A Level Maths tutor, ...

8 months ago

Answered by Linetta, an A Level Maths tutor with MyTutor


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

270 SUBJECT SPECIALISTS

£20 /hr

Iebad A.

Degree: Aerospace Engineering (Masters) - Sheffield University

Subjects offered:Maths, Italian

Maths
Italian

“About me: Hello, my name is Iebad and I am an aerospace engineering student at The University of Sheffield. As an engineer, maths is the key to unlock all the solutions to our problems in this field. Since the early years I had a broad...”

£24 /hr

Runzhi C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi there, I am a first year medical student at Imperial College London and I have lived in the UK all my life. I enjoy studying medicine because it encompasses both scientific knowledge and social aspects. I am relatively new to tutor...”

£20 /hr

Oliver V.

Degree: Mathematics (Masters) - Oxford, St John's College University

Subjects offered:Maths, Chemistry+ 4 more

Maths
Chemistry
Biology
.MAT.
-Personal Statements-
-Oxbridge Preparation-

“University of Oxford Mathematics student enthusiastic about improving grades and preparing for entrance exams”

About the author

£20 /hr

Linetta A.

Degree: Mathematics & Philosophy (Bachelors) - Bristol University

Subjects offered:Maths, Religious Studies+ 1 more

Maths
Religious Studies
Philosophy and Ethics

“Hi! My name is Nettie, and I’m just about to go into my second year studying Maths & Philosophy at the University of Bristol. Maths I can’t remember a time when I wasn’t obsessed with numbers and solving problems, and I hope I can in...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Differentiate x^5 + 3x^2 - 17 with respect to x

Use logarithms to solve 9^x=15

x = 2t + 5, y = 3 + 4/t. a) Find dy/dx at (9.5) and b) find y in terms of x.

Outline the various ways that you can differentiate a function

View A Level Maths tutors

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

mtw:mercury1:status:ok