An angle φ satisfies sinφ=−1312.
a. (i) State the possible quadrants in which φ can lie, giving reasons based on the signs of the trigonometric ratios.
b. (ii) Explain how the sign of cosφ is fixed when it is additionally known that π<φ<23π. Briefly justify your answer with reference to quadrant signs.
c. (iii) Using the information above, calculate cosφ and tanφ.
d. (iv) Verify that sin2φ+cos2φ=1 for the values obtained.