Misreading a standard trigonometric value

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

1. 01

   Find the exact value of the expression below. $\displaystyle \tan\!\left(\frac{5\pi}{6}\right)\sec\!\left(\frac{\pi}{3}\right)$

   ·Functions, graphs and inverses·Introductory

2. 02

   Find the exact value of $\arctan\!\left(\tan\dfrac{3\pi}{4}\right)$.

   ·Implicit differentiation and inverse trigonometric functions·Introductory

3. 03

   A person’s core body temperature, in degrees Celsius, is modelled by the function below, where $t$ is the time in hours after midnight. At what time $t$, with $0 \leq t < 24$, is the temperature highest? $\displaystyle T(t) = 36.9 + 0.4\sin\!\left(\frac{\pi}{12}(t - 11)\right)$

   ·Power functions and first sketches·Standard

4. 04

   Find the $y$-intercept of the line tangent to $y = \sin x + 3x$ at $x = \pi$.

   ·Exponential and trigonometric functions·Standard

5. 05

   Let $g(x) = x^{2}\sin(3x)$. Find $g'\!\left(\dfrac{\pi}{3}\right)$.

   ·The chain rule and logarithms·Standard